Nearly five months after DuPont’s chairwoman and chief executive, Ellen Kullman, beat back a challenge from a longtime activist investor, she is finding herself heading for the exit.

DuPont said on Monday afternoon that Ms. Kullman, who is 59, would step down on Oct. 16, while conceding that it would have to cut its earnings forecast and accelerate a cost-cutting plan.

Shares of DuPont surged 6 percent in after-hours trading.

Ms. Kullman will be replaced on an interim basis by Edward D. Breen, who is also 59, a former executive at Tyco, who joined the chemical manufacturer’s board in February under pressure from the activist investor Nelson Peltz.

Mr. Peltz and his investment firm, Trian Fund Management, fought a rare public battle against DuPont, the 213-year-old chemical manufacturer and maker of Kevlar and Teflon. Trian, insisting that DuPont needed change because it had repeatedly missed financial targets and still carried plenty of costs worth cutting, sought four board seats.

Many corporate boards in recent years have sought to settle with activists, aware of such investors’ growing appeal with mutual funds and other shareholders. These hedge fund managers have gained ever more success — and ambition: Trian itself disclosed on Monday that it had become one of the biggest shareholders in General Electric, and urged the industrial conglomerate to buy back more shares and take on more debt.

But Ms. Kullman took the unusual step of digging in and fighting against one of Wall Street’s best-known corporate dissidents, who has often gained board seats and prompted change without picking a public fight.

After several months of bitter public arguments and spurned settlement offers, DuPont ultimately prevailed in a shareholder vote on its board. But even those close to the company conceded that the investor base included a larger-than-normal group of individual investors, who largely back management teams.

“As our chair and C.E.O., Ellen led DuPont through the global recession and the dramatic transformation of the last several years with the highest standard of integrity and commitment,” Alexander Cutler, DuPont’s lead independent director, said in a statement.

Yet even at the time of Ms. Kullman’s victory, investors expressed some disappointment in Trian’s failure. The big California pension fund known as Calstrs said it was “disappointed” in the outcome. And shares in DuPont fell nearly 7 percent after the election’s results were revealed.

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The company’s stock has fallen about 27 percent for the year to date, giving DuPont a market value of about $44.6 billion.

During that fight, Trian repeatedly criticized the company for missing financial performance targets. Ms. Kullman’s response consistently has been that the company had beaten major stock indexes.

Yet in announcing her departure, DuPont conceded that it had yet again fallen short, this time blaming the strength of the United States dollar and a weakening of agricultural markets in Brazil and other areas that reduced demand.

The company said that it was cutting the outlook for its operating earnings for the full year to $2.75 a share from $3.10.

DuPont, formally the E. I. du Pont de Nemours & Company, also said that it planned to accelerate its cost savings initiative by one year, aiming to reap $1.3 billion by the end of 2016.

“As macro conditions have deteriorated further, we are intensifying our effort to offset these pressures with further productivity improvements and cost savings, while making disciplined and targeted investments in innovation to increase value for shareholders over the long term,” Nicholas C. Fanandakis, the company’s chief financial officer, said in a statement.

A representative for Trian declined to comment on the departure of Ms. Kullman.

A version of this article appears in print on October 6, 2015, on Page B2 of the New York edition with the headline: DuPont Chief Stepping Down, Under Investor Pressure. Order Reprints|Today's Paper|Subscribe